Optical suppression of tilt-to-length coupling in the LISA long-arm interferometer
M Chwalla, K Danzmann, M Dovale Álvarez, J J Esteban Delgado, G Fernández Barranco, E Fitzsimons, O Gerberding, G Heinzel, C J Killow, M Lieser, M Perreur-Lloyd… 展开作者
M Chwalla, K Danzmann, M Dovale Álvarez, J J Esteban Delgado, G Fernández Barranco, E Fitzsimons, O Gerberding, G Heinzel, C J Killow, M Lieser, M Perreur-Lloyd, D I Robertson, J M Rohr, S Schuster, T S Schwarze, M Tröbs, G Wanner, H Ward
The arm length and the isolation in space enable LISA to probe for signals unattainable on ground, opening a window to the sub-Hz gravitational-wave universe. The coupling of unavoidable angular spacecraft jitter into the longitudinal displacement measurement, an effect known as tilt-to-length (TTL) coupling, is critical for realizing the required sensitivity of picometer$/\sqrt{\rm{Hz}}$. An ultra-stable interferometer testbed has been developed in order to investigate this issue and validate mitigation strategies in a setup representative of LISA, and in this paper it is operated in the long-arm interferometer configuration. The testbed is fitted with a flat-top beam generator to simulate the beam received by a LISA spacecraft. We demonstrate a reduction of TTL coupling between this flat-top beam and a Gaussian reference beam via introducing two- and four-lens imaging systems. TTL coupling factors below $\pm 25\,μ$m/rad for beam tilts within $\pm 300\,μ$rad are obtained by careful optimization of the system. Moreover we show that the additional TTL coupling due to lateral alignment errors of elements of the imaging system can be compensated by introducing lateral shifts of the detector, and vice versa. These findings help validate the suitability of this noise-reduction technique for the LISA long-arm interferometer.
Objects sensed by laser interferometers are usually not stable in position or orientation. This angular instability can lead to a coupling of angular tilt to apparent longitudinal displacement -- tilt-to-length coupling (TTL). In LISA this is a potential noise source for both the test mass interferometer and the long-arm interferometer. We have experimentally investigated TTL coupling in a setup representative for the LISA test mass interferometer and used this system to characterise two different imaging systems (a two-lens design and a four-lens design) both designed to minimise TTL coupling…
The Laser Interferometer Space Antenna is a foreseen space-based gravitational wave detector, which aims to detect 10^20 strains in the frequency range from 0.1 mHz to 1 Hz. It is a triangular constellation of three spacecraft, with equal sides of 2,5 x 10^9 m, where every spacecraft hosts a pair of telescopes that simultaneously transmit and receive laser beams measuring the constellation arms by heterodyning the received wavefronts with local references. Due to the spacecraft and constellation jitters, the interfering (received and local) wavefronts become misaligned. We investigate analytic…
Entangled light can provide a seminal improvement in resolution sensitivity even without achieving Heisenberg limit in a single channel. In this paper, based on the back-of-the-envelope type calculations, I demonstrate an alternative path to space based long-arm interferometer. Its advantage with respect to LISA is that it does not require complex satellites with many active components to achieve similar resolution.
The Laser Interferometer Space Antenna is a foreseen gravitational wave detector, which aims to detect $10^{-20}$ strains in the frequency range from 0.1 mHz to 1 Hz. It is a triangular constellation, with equal sides of $2,5 \times 10^9$ m, of three spacecraft, where heterodyne interferometry measures the spacecraft distances. The stray light from the powerful transmitted beam can overlap with the received one and interfere with the heterodyne signal. We investigated the contribution of random phase variations of the stray photons to the noise of the heterodyne signal. A balanced detection sc…
We present recent sensitivity measurements of the LISA Technology Package interferometer with articulated mirrors as test masses, actuated by piezo-electric transducers. The required longitudinal displacement resolution of 9 pm/sqrt[Hz] above 3 mHz has been demonstrated with an angular noise that corresponds to the expected in on-orbit operation. The excess noise contribution of this test mass jitter onto the sensitive displacement readout was completely subtracted by fitting the angular interferometric data streams to the longitudinal displacement measurement. Thus, this cross-coupling consti…
The Laser Interferometer Space Antenna (LISA) aims to observe gravitational waves in the mHz regime over its 10-year mission time. LISA will operate laser interferometers between three spacecrafts. Each spacecraft will utilize independent clocks which determine the sampling times of onboard phasemeters to extract the interferometric phases and, ultimately, gravitational wave signals. To suppress limiting laser frequency noise, signals sampled by each phasemeter need to be combined in postprocessing to synthesize virtual equal-arm interferometers. The synthesis in turn requires a synchronizatio…
The Laser Interferometer Space Antenna (LISA) is a future space-based interferometric gravitational-wave detector consisting of three spacecraft in a triangular configuration. The interferometric measurements of path length changes between satellites will be performed on optical benches in the satellites. Angular misalignments of the interfering beams couple into the length measurement and represent a significant noise source. Imaging systems will be used to reduce this tilt-to-length coupling. We designed and constructed an optical test bed to experimentally investigate tilt-to-length couplin…
Mathematical derivation and verification of the amplitude of LISA's interferometric signals on an ultra-stable interferometer testbed
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；University of Granada（格拉纳达大学）
The Laser Interferometer Space Antenna (LISA) is a future space-based gravitational wave (GW) detector designed to be sensitive to sources radiating in the low frequency regime (0.1 mHz to 1 Hz). LISA's interferometer signals will be dominated by laser frequency noise which has to be suppressed by about 7 orders of magnitude using an algorithm called Time-Delay Interferometry (TDI). Arm locking has been proposed to reduce the laser frequency noise by a few orders of magnitude to reduce the potential risks associated with TDI. In this paper, we present an updated performance model for arm locki…
Tilt-to-length (TTL) noise from angular jitter in LISA is projected to be the dominant noise source in the milli-Hertz band unless corrected in post-processing. The correction is only possible after removing the overwhelming laser phase noise using time-delay interferometry (TDI). We present here a frequency domain model that describes the effect of angular motion of all three spacecraft on the interferometric signals after propagating through TDI. We then apply a Fisher information matrix analysis to this model to calculate the minimum uncertainty with which TTL coupling coefficients may be e…
Space-based gravitational wave detectors based on the Laser Interferometer Space Antenna (LISA) design operate by synthesizing one or more interferometers from fringe velocity measurements generated by changes in the light travel time between three spacecraft in a special set of drag-free heliocentric orbits. These orbits determine the inclination of the synthesized interferometer with respect to the ecliptic plane. Once these spacecraft are placed in their orbits, the orientation of the interferometers at any future time is fixed by Kepler's Laws based on the initial orientation of the spacec…
We report on the first demonstration of time-delay interferometry (TDI) for LISA, the Laser Interferometer Space Antenna. TDI was implemented in a laboratory experiment designed to mimic the noise couplings that will occur in LISA. TDI suppressed laser frequency noise by approximately 10^9 and clock phase noise by 6x10^4, recovering the intrinsic displacement noise floor of our laboratory test bed. This removal of laser frequency noise and clock phase noise in post-processing marks the first experimental validation of the LISA measurement scheme.
LISA Non-Linear Dynamics and Tilt-To-Length Coupling
Universität Heidelberg（海德堡大学）；KU Leuven（荷语鲁汶大学）；Leuven Gravity Institute, KU Leuven（荷语鲁汶大学引力研究所）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）
LISA Pathfinder is a technology demonstration mission for the Laser Interferometer Space Antenna (LISA). The main experiment on-board LISA Pathfinder is the so-called LISA Technology Package (LTP) which has the aim to measure the differential acceleration between two free-falling test masses with an accuracy of 3x10^(-14) ms^(-2)/sqrt[Hz] between 1 mHz and 30 mHz. This measurement is performed interferometrically by the Optical Metrology System (OMS) on-board LISA Pathfinder. In this paper we present the development of an experimental end-to-end testbed of the entire OMS. It includes the inter…
We explore the prospects for the detection of giant circumbinary exoplanets and brown dwarfs (BDs) orbiting Galactic double white dwarfs binaries (DWDs) with the Laser Interferometer Space Antenna (LISA). By assuming an occurrence rate of 50%, motivated by white dwarf pollution observations, we built a Galactic synthetic population of P-type giant exoplanets and BDs orbiting DWDs. We carried this out by injecting different sub-stellar populations, with various mass and orbital separation characteristics, into the DWD population used in the LISA mission proposal. We then performed a Fisher matr…
The OSE (Offline Simulations Environment) simulator of the LPF (LISA Pathfinder) mission is intended to simulate the different experiments to be carried out in flight. Amongst these, the thermal diagnostics experiments are intended to relate thermal disturbances and interferometer readouts, thereby allowing the subtraction of thermally induced interferences from the interferometer channels. In this paper we report on the modelling of these simulated experiments, including the parametrisation of different thermal effects (radiation pressure effect, radiometer effect) that will appear in the Ine…
The LISA Pathfinder mission to space employs an optical metrology system (OMS) at its core to measure the distance and attitude between two freely floating test-masses to picometer and nanorad accuracy, respectively, within the measurement band of [1 mHz, 30 mHz]. The OMS is based upon an ultra-stable optical bench with 4 heterodyne interferometers from which interference signals are read-out and processed by a digital phase-meter. Laser frequency noise, power fluctuations and optical path-length variations are suppressed to uncritical levels by dedicated control loops so that the measurement …
The Laser Interferometer Space Antenna (LISA) and its metrology chain have to fulfill stringent performance requirements to enable the space-based detection of gravitational waves. This implies the necessity of performance verification methods. In particular, the extraction of the interferometric phase, implemented by a phasemeter, needs to be probed for linearity and phase noise contributions. This Letter reports on a hexagonal quasimonolithic optical bench implementing a three-signal test for this purpose. Its characterization as sufficiently stable down to picometer levels is presented as w…
Tilt-to-length coupling is a technical term for the cross-coupling of angular or lateral jitter into an interferometric phase signal. It is an important noise source in precision interferometers and originates either from changes in the optical path lengths or from wavefront and clipping effects. Within this paper, we focus on geometric TTL coupling and categorize it into a number of different mechanisms for which we give analytic expressions. We then show that this geometric description is not always sufficient to predict the TTL coupling noise within an interferometer. We, therefore, discuss…
We propose a Geostationary Gravitational Wave Interferometer (GEOGRAWI) mission concept for making observations in the sub-Hertz band. GEOGRAWI is expected to meet some of LISA's science goals in the lower part of its accessible frequency band ($10^{-4} - 2 \times 10^{-2}$ Hz), and to outperform them by a large margin in the higher-part of it ($2 \times 10^{-2} - 10$ Hz). As a consequence of its Earth-bound orbit, GEOGRAWI is significantly less expensive than the interplanetary LISA mission and could be either an entirely US mission or managed and operated by NASA in partnership with the Brazi…
Laser frequency stabilization is a critical part of the interferometry measurement system of space-based gravitational wave observatories such as the Laser Interferometer Space Antenna (LISA). Arm locking as a proposed frequency stabilization technique, transfers the stability of the long arm lengths to the laser frequency. The arm locking sensor synthesizes an adequately filtered linear combination of the inter-spacecraft phase measurements to estimate the laser frequency noise, which can be used to control the laser frequency. At the University of Florida we developed the hardware-based Univ…
One of the atom interferometer gravitational wave missions proposed by Dimopoulos et al.1 in 2008 was called AGIS-Sat. 2. It had a suggested gravitational wave sensitivity set by the atom state detection shot noise level that started at 1 mHz, was comparable to LISA sensitivity from 1 to about 20 mHz, and had better sensitivity from 20 to 500 mHz. The separation between the spacecraft was 1,000 km, with atom interferometers 200 m long and shades from sunlight used at each end. A careful analysis of many error sources was included, but requirements on the time-stability of both the laser wavefr…
The Laser Interferometer Space Antenna (LISA) is a European Space Agency mission that aims to measure gravitational waves in the millihertz range. The three-spacecraft constellation forms a nearly-equilateral triangle, which experiences flexing along its orbit around the Sun. These time-varying and unequal armlengths require to process measurements with time-delay interferometry (TDI) to synthesize virtual equal-arm interferometers, and reduce the otherwise overwhelming laser frequency noise. Algorithms compatible with such TDI combinations have recently been proposed in order to suppress the …
The geosynchronous Laser Interferometer Space Antenna (gLISA) is a space-based gravitational wave (GW) mission that, for the past five years, has been under joint study at the Jet Propulsion Laboratory, Stanford University, the National Institute for Space Research (I.N.P.E., Brazil), and Space Systems Loral. If flown at the same time as the LISA mission, the two arrays will deliver a joint sensitivity that accounts for the best performance of both missions in their respective parts of the mHz band. This simultaneous operation will result in an optimally combined sensitivity curve that is "whi…
Space-based gravitational-wave observatories such as the Laser Interferometer Space Antenna (LISA) use time-shifted and time-scaled linear combinations of differential laser-phase beat signals to cancel the otherwise overwhelming laser frequency noise. Nanosecond timing precision is needed to accurately form these Time-Delay Interferometry (TDI) combinations which defines a ~1 meter requirement on the inter-spacecraft ranging capability. The University of Florida Hardware-in-the-loop LISA Interferometry Simulator (UFLIS) has been used to test Time-Delay Interferometry in a configuration which …
Arm locking is a technique that has been proposed for reducing laser frequency fluctuations in the Laser Interferometer Space Antenna (LISA), a gravitational-wave observatory sensitive in the milliHertz frequency band. Arm locking takes advantage of the geometric stability of the triangular constellation of three spacecraft that comprise LISA to provide a frequency reference with a stability in the LISA measurement band that exceeds that available from a standard reference such as an optical cavity or molecular absorption line. We have implemented a time-domain simulation of arm locking includ…
One source of noise for the Laser Interferometer Space Antenna (LISA) will be time-varying changes of the space environment in the form of solar wind particles and photon pressure from fluctuating solar irradiance. The approximate magnitude of these effects can be estimated from the average properties of the solar wind and the solar irradiance. We use data taken by the ACE (Advanced Compton Explorer) satellite and the VIRGO (Variability of solar IRradiance and Gravity Oscillations) instrument on the SOHO satellite over an entire solar cycle to calculate the forces due to solar wind and photon …
Construction of Sensitivity Curves for Dynamic LISA and Taiji
School of Astronomy and Space Science, University of Chinese Academy of Sciences (UCAS)（中国科学院大学天文与空间科学学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础物理与数学学院）；International Centre for Theoretical Physics Asia-Pacific, UCAS（中国科学院大学亚太理论物理中心）
